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In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure .
The compressibility factor is defined as = where p is the pressure of the gas, T is its temperature, and is its molar volume, all measured independently of one another. In the case of an ideal gas, the compressibility factor Z is equal to unity, and the familiar ideal gas law is recovered:
According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree. [1] [2]
Where p is the pressure, T is the temperature, R the ideal gas constant, and V m the molar volume. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature ( T c ) and critical pressure ( p c ) using these relations:
In general, compressibility is defined as the relative volume change of a fluid or solid as a response to a pressure, and may be determined for substances in any phase. Similarly, thermal expansion is the tendency of matter to change in volume in response to a change in temperature.
The largest and the lowest solution are the gas and liquid reduced volume. In this situation, the Maxwell construction is sometimes used to model the pressure as a function of molar volume. The compressibility factor = / is often used to characterize non-ideal behavior. For the van der Waals equation in reduced form, this becomes
These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor, provide the basis for the simplest form of the theorem of corresponding states. [1] Reduced properties are also used to define the Peng–Robinson equation of state, a model designed to provide reasonable accuracy near the critical point. [2]
The general equation of state for a real gas is usually written as = = where the critical compressibility factor , which reflects the volumetric deviation of the real gases from the ideal gas, is also not easily accessible from laboratory experiments. However, critical pressure and critical temperature are more accessible from measurements.